Transparent media capable of photoinduced refractive index changes and their application to light guides and the like

ABSTRACT

THERE ARE DISCLOSED A VARIETY OF METHODS FOR PRODUCING LIGHT GUIDES INSUITABLE SENSITIZED SAMPLES UPON IRRADIATION WITH FOCUSED ULTRAVIOLET LIGHT AND SUBSEQUENT AGING. THESE METHODS ARE BASED UPON THE RECOVERY THAT ULTRAVIOLET RADIATION FROM A MERCURY ARC AT 3650 A. OR FROM AN ULTRAVIOLET HELIUM-CADMIUM ION LASER AT 3250 A. PRODUCES READILY OBSERVABLE IRREVVERSIBLE INDEX OF REFRACTION CHANGES IN POLY(METHYL METHACRYLATE) POLYMERIZED AT LOW TEMPERATURES OF AROUND 40-50 DEGRESS CENTIGRADE. UPON SUBSEQUENT AGING THE AMOUNT AND GRADIENT OF THE INDEX CHANGE SUBSTANTIALLY INCREASE.

350*9fio12 FTHSE XR 315099635 May 7. 3974 E A, CHANDROSS E'IAL 3,809,68$

IRANSPARBN'I MEDIA CAPABLE OF PHOTO-INDUCED REFRACIIVE I'N'DEA CHANGESAND THEIR APPLICATION TO LIGHT GUIDES AND THE LIKE Original Filed March19. 1970 3 Sheets-Sheet 1 FIG. SENSITIZED SAMPLE WRITTEN OPTICAL GUIDEULTRAVIOLET LASER BEAM SOURCE v. r TRANSLATING H MECHANISM I4 u.v.-MICROSCOPE OBJECTIVE FIG. 2

NON-COUPLING SEPARATION AT cRoss-ovER OPTIONAL 3 sECONO LIGHT sOuRCE 3eFIRST COUPLING UTILIZATION SEPARATION 33 APPAgfATU s E I OPTIONAL I IRsTLIGHT sECONO sOuRCE OTI LIzATION I 34 APPA3R7ATUS May 7, 1974 5 oss ErAL3,809,686

TRANSPARENT MEDIA CAPABLE OF PHOTO-INDUCED REFRACTIVE INDEX p OHANGESAND THEIR APPLICATION TO LIGHT GUIDES AND THE LIKE )rlg1n3l Flled March19, 1970 5 Sheets-Sheet 2 FIG. 4

FOCUSING 42 TI I HOLOGRAM EXPOSED 3-D F M LIGHT GUIDE sENsITIzED NETWORKSAMPLE 44 SUPPLY F/G.5 SPOOL TAKE-UP SPOOL TENsIoN 57 ADJUSTMENT IGU|DANCE LIQUID 52 3 MATCHED To FIBER uLTRAvIoLET LASER DRIvE AND SOURCEGUIDANCE RoLLER 59 5e u.v LENs k 58 BS8RER TRANSVERSE A A CONTEAII NERINDEX 60 GRADIENT INDUCED FIG. 6

FORM PATTERN BY COMPLETE PATTERN 5mm? IRRIDATING wITII INDEX GRADIENTSFOCUSED U.V. LIGHT eg BY AGING May 7. 1974 CHANDRQSS ETAL 3,809,686

TRANSPARENT MEDIA CAPABLE OF PHOTO-INDUCED REFRACIIVE INDEX CHANGES ANDTHEIR APPLICATION TO LIGHT GUIDES AND THE LIKE Original Filed March 19,1970 3 Sheets-Sheet 3 PLANAR uv LASER 7 BEAM PLANAR UV LASER BEAM -72SOURCE PLANAR uv LASER BEAM SOURCE SAMPLE 2n SIN 9 PLANAR UV LASER BEAMSOURCE United States Patent O US. Cl. 260-895 A 3 Claims ABSTRACT OF THEDISCLOSURE There are disclosed a variety of methods for producing lightguides in suitably sensitized samples upon irradiation with focusedultraviolet light and subsequent aging. These methods are based upon thediscovery that ultraviolet radiation from a mercury are at 3650 A. orfrom an ultraviolet helium-cadmium ion laser at 3250 A. produces readilyobservable irreversible index of refraction changes in poly(methylmethacrylate) polymerized at low temperatures of around 40-50 degreescentigrade. Upon subsequent aging, the amount and gradient of the indexchange substantially increase.

This application is a division of application Ser. No. 21,102, filedMar. 19, 1970, now US. Pat. No. 3,689,264.

BACKGROUND OF THE INVENTION This invention relates to methods andapparatus for producing light guides and other patterns of elevatedindex of refraction in transparent bodies, particularly to opticalmethods for producing such light guides and patterns.

It has heretofore been proposed to produce guiding changes of index ofrefraction in transparent bodies by making the body with suitablechanges in composition transversely along the proposed guiding path andby highenergy methods of damaging the transparent body, for example byneutron radiation. All these techniques are difficult to implement inpractice. and have not been found attractive. The problems of writinglight guides'into dielectric materials are discussed in the article byS. E. Miller in the Bell System Technical Journal, vol. 48, p. 2063(September 1969).

SUMMARY OF THE INVENTION Our invention is based upon the discovery of anoptical method for producing light guides and other patterns of elevatedindex of refraction in suitably sensitized transparent bodies byirradiating the body with focused ultraviolet light.

Specifically, our invention involves the discovery that ultravioletradiation from a mercury are at 3650 A. or from a helium-cadmium ionlaser at 3250 A., both in the ultra-violet, produces readily observableirreversible index of refraction changes in poly(methyl methacrylate)sensitized by the addition of ingredients to enable photoinducedcross-linking. The poly(methyl methacrylate) is prepared from methylmethacrylate polymerized at low temperatures of about 40-50 degreescentigrade after addition of the sensitizing ingredient. The sensitizingmaterials are apparently rendered ineffective by higher temperatures,the subsequent irradiation effect could not be observed in samplespolymerized at or heated to substantially higher temperatures.

In addition, in the preparation of our samples, an appropriate amount(-25 mg. per 100 ml.) of a selected 3,809,686 Patented May 7, 1974 iceinitiator may be included to facilitate polymerization so far as thatdoes not impair the sensitization. The initiator and its products shouldnot absorb the exposing radiation; whereas the sensitizing ingredient orthe polymer does. Some polymers of methyl methacrylate sensitized andprepared without an initiator also exhibit a comparable effect, in thatultraviolet radiation increases the index of refraction.

While optical changes in index of refraction in dielectric bodies suchas lithium niobate have heretofore been observed in the presence ofvisible or ultraviolet radiation, the present effect involves afundamentally different phenomenon producing much greater andirreversible fractional changes in index of refraction and also involvesa subsequent completion of the index-of-refraction gradient not known inthe previously employed types of optical damage. This completion isprobably a relaxation of strain set up by the stresses of photo-inducedcrosslinking of polymers, so that while the initial exposure iseffective to start the index change, the amount and gradient of theindex change are subsequently substantially increased by a suitable stepas aging. Preferably, the aging is continued until a stable condition isachieved.

The index change characteristic of our invention is tentativelyattributed to ulraviolet-induced cross-linking of the polymer chains tochange the density of the material. Further, some species of ourinvention employ peroxides as the sensitizing ingredients. Nevertheless,our invention should not be construed to depend upon the accuracy of thetentative explanation.

BRIEF DESCRIPTION OF THE DRAWING 'Further features and advantages of ourinvention will become apparent from the following detailed description,taken together with the drawing, in which;

FIG. 1 is a partially pictorial and partially block diagrammaticillustration of an apparatus for performing the exposure step of onespecific method according to our invention;

FIG. 2 is a pictorial illustration of a sample in which two light guideshave been Written according to our invention so that they cross overwith a non-coupling separation therebetween;

FIG. 3 is a partially pictorial and partially block diagrammaticillustration of one type of apparatus in which light guides according toour invention may be used as a directional coupler;

FIG. 4 is a partially pictorial and partially block diagrammaticillustration of an apparatus for practicing the the exposure step of asecond specific method according to our invention;

FIG. 5 is a partially pictorial and partially block diagrammaticillustration of an apparatus for practicing the exposure step of a thirdspecific method according to our invention;

FIG. 6 is a flow chart of the basic steps involved in the practice ofour invention;

FIG. 7 is a partially pictorial and partially block d-iagrammaticillustration of an apparatus for exposing a sample to make a reflectorby the method of our invention; and

FIG. 8 is a modification of the illustration of FIG. 7 to generalize itsapplicability.

DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS In FIG. 1 ultraviolet light froma suitable source 11 is focused by an ultraviolet transmittingmicroscope objective 12 to a desired region within (although it couldalso be upon the surface of) a suitably sensitized sample 13 which istranslated transversely to the focused ultraviolet beam by a translatingmechanism 14.

The ultraviolet laser beam source 11 is illustratively an ultravioletcadmium ion laser operating at 3250 A. units, although in someexperiments it was replaced by a mercury arc lamp operating at 3650 A.units. It may include suitable lenses for collimating the beam.Ultraviolet microscope objective 12 is of conventional type and includesan apertured reflecting element 15 and the convex reflecting element 16,which together bring the entire beam to a sharp focus at approximatelytwice the distance from reflector 15 as is reflector 16. A quartzrefracting objective would also be suitable.

The sample 13 is translated through the focused beam by means of thetranslating mechanism 14, which may include rack-and-screw mechanismsadapted for translation of sample 13 in three orthogonal directions.lllustratively, one part of mechanism 14 is rigidly mounted with sample13 in order to provide coupling of the prescribed motion to sample 13.

The apparatus of FIG. 1 was employed to practice the exposure step of afirst specific method accordingto our invention as follows. First, thesample 13 was prepared in an evacuated capsule by polymerizing methylmethacrylate, including sensitizing peroxides, at low temperaturesaround 50 degrees centigrade with azobisisobutyronitride, (CHC(CN)N=N-C(CN)(CH as a polymerization initiator (5-25 mg. per 100 ml.)and without any additives to stabilize the poly(methyl me-thacrylate)against ultraviolet damage. This initiator is sometimes called AIBN. Thesample was then mounted upon the mating part of translating mechanism 14and disposed at the focuse of ultraviolet microscope objective 12.Illustratively, the optical guide was written through the bulk of sample13 by the motion of translating mechanism 14 and was continued to twolateral surfaces thereof. To write a guide of that nature, thetranslating mechanism 14 was caused to produce a desired set ofcontinuous motions of sample 13. While control of the servomotors oftranslating mechanism 14 was done manually in our experiments, it couldalso be done by a programmed digital computer. Even before the agingstep, there was obtained a continuous optical guiding path in sample 13for a light of comparable or lower frequency, which could be introducedcollinearly at an end of the path by a suitable lens. The path isillustratively shown, partially written, as the optical guide 17 insample 13 in FIG. 1.

Upon completion of the translation of sample 13, it was removed from thefocus of the ultraviolet laser beam and set aside to age. After thepassage of. several hours, the amount and gradient of refractive indexchange were found to have substantially increased. The incrementalchange produced by this aging process tends to diminish with time to astable condition. The desirable aging time depends on the dimensions ofthe irradiated region. The total index change produced by this methodwas sufficiently large to allow bends of radius of one centimeter, whichis as small as might be required in applications.

Using interferometric techniques, we have determined that forirradiation with 3650 A. ultraviolet light from the mercury arc, theinduced index change is about An=V2 l0- E, where E is the exposure injoules per square centimeter. For irradiation with 3250 A. light from acadmium ion laser, the index change is at least An==l E', and thisrelationship appears to hold up to values of An=3 1'0 Resolutions up to5000 lines per millimeter have been observed. Our study has indicatedthat a large number of other plastics; especially other acrylates,should exhibit similar behavior, and other sensitizing ingredients arefeasible and include those that readily promote cross-linking. I

In some of these other substances or in any of these substancesincluding different sensitizers, radiation at wavelengths outside theultraviolet band, but otherwise employed according to the exposure stepsof the present invention, may also be able to induce the index change.

With respect to other starting materials for sample 13, suitablesensitization of the sample before exposure and, to a lesser degree,completion of its refractive index gradient after exposure appear to besignificant and may also be useful in related methods of writing opticalguides such as those employing particle irradiation by electrons orneutrons.

Employing the embodiment of FIG. l, we have experimentally demonstratedthat fine (about one to 22 micrometers wide) light guides can beproduced inside the plastic or on its surface by focusing theultraviolet light as in FIG. 1 and translating the sample 13 along adesired path. The sample is then subsequently aged, as previouslydescribed. Both straight and curved guides, the latter having as smallas about one centimeter radius of curvature, have been made to guide a6328 A. red beam from a helium-neon laser. In principle, any light offrequency substantially different from those to which the sample hasbeen sensitized may be successfully guided by being focused into an endsurface of the guide in the sample 13. In addition, light of the samewavelength as the exposing light can be guided if the surroundingmaterial has first been made suificienty insensitive to furtherexposure.

When visible light was focused into the guides in our experiments,optical waveguide mode patterns were observed in the transmitted lightas observed when extracted from the guide; and for a straight guide 1centimeter long at least percent of the incident light has been observedin the transmitted fundamental mode. Much of the mode loss may be theresult of input and output coupling losses, which can be readilyreduced.

With respect to the three steps employed in the method of FIG. 1, thefollowing parameters appear to be pertinent.

In the sensitizing step, the methylmcthacrylate is either autoxidizedslowly or is subjected to diffuse ultraviolet radiation from alow-pressure mercury lamp in the presence of oxygen. The monomer thusobtained can then be polymerized with or without an initiator, so longas the sensitizing ingredient is not impaired. It is apparentlydesirable that the poly(methyl methacrylate) be polymerized attemperatures substantially below degrees centigrade, since the effectthat we employ could not be observed in samples that had beenpolymerized at 100 degrees centigrade, or that had been heated briefly(one hour) to degrees centigrade. The best temperature of polymerizationis apparently about 40-50 degrees centi' grade but may range as low asnearly 25 degrees centigrade without being undesirably slow and as highas 75 degrees centigrade without substantial loss of sensitization.

It is also possible to sensitize the samples by the addition ofperoxides, such as dicumyl peroxide or tertiarybutyl perbenzoate.Typically, these peroxides have been added before polymerization butmight be added to sufficiently thin samples after polymerization.

In the exposure step, it appears desirable to focus the light beam assharply as possible, or at least to a degree that the desiredindex-of-refraction gradient across the guide will be automaticallyprovided by the cross-sectional characteristics of the light at thewaist of the beam and by its convergence and divergence from that waist.Of course, it should be noted that the diameter and axial extent of thebeam waist can be adjusted by varying the angle of convergence of theincident ultraviolet beam. Thus, if a guide of larger cross section isdesired, that angle of convergence can be decreased so that the beamwaist diameter increases.

In the aging step, the parameters do not appear to be critical. We havefound good results simply by leaving the exposed samples in a dark placeat a temperature below about 60 degrees centigrade for a period ofseveral days. The minimum period of aging desirable can be very smallfor small irradiated regions; and the maximum period of aging thatappears to be desirable is one week, after which negligible changeoccurs.

With respect to the use of the guide thus produced, it may be noted thatthe wavelength of the light to be guided is preferably outside thewavelength range of photosensitivity, which encompasses the wavelengthof the ultraviolet light which exposed the sample 13, in order to avoidfurther change in the cross-sectional variation of index of refractionwithin the guide. For poly(methyl methacrylate), we prefer that thewavelength of light to be guided be longer than about 4000 A.

A typical product of the methods of FIG. 1 is shown in FIG. 2. Thesensitized and then exposed sample 21 has the nonintersecting opticalguides 22 and 23 written therein by the method of FIG. 1. Guides 22 and23 typically have an index gradient across their cross sections of about3 l0- and have an effective diameter of 2 micrometers. The guides 22 and23 in both cases extend to opposite surfaces of the sample 21 and have areparation at their crossover, that is, at the region of their minimumseparation, which is at least micrometers, for example 50 micrometers,between their limits defined by their effective diameters. Thisseparation is a noncoupling separation, which means that there isnegligible exchange of light energy between the guides 22 and 23 whenthe wavelength of the light propagated therein is less than onemicrometer.

Another typical product of the method of FIG. 1 is shown in FIG. 3. Thesensitized and exposed sample 31 of polymethyl methacrylate has theguides 32 and 33 therein, which have parameters similar to guides 22 and23 of FIG. 2. The principal difference from the sample of FIG. 2 is thatin the sample 31 of FIG. 3 the light guides 32 and 33 are separated byless than 10 micrometers, e.g., one micrometer, so that substantialcoupling of light between the guides occurs when the wavelength of thelight is at least as long as 0.4 micrometer (4000 A.).

It will be noted that this coupling between the guides 32 and 33 is adirectional coupling so that light from a first source 34 introduced atone end of guide 32 is coupled into guide 33 to propagate in such adirection that it emerges eventually to propagate toward the firstutilization apparatus 35. On the other hand, light from the optionalsecond light source 36, used in the absence of source 34 and directedinto the opposite end of guide 32, is coupled into guide 33 to propagatetherein in such a direction that it eventually emerges therefrom topropagate toward the optional second utilization apparatus 37.

More broadly, the circuit aspects of the use of products made accordingto the method of our invention are covered in more detail in articles byE. A. I. Marcatili in the Bell System Technical Journal, vol. 48, p.2071 (September 1969) and vol. 48, p. 2103 (September 1969).

A second specific exposure step of a method according to our inventionis practiced with the apparatus shown in FIG. 4.

In FIG. 4, a source 41 of a broad ultraviolet coherent beam is directedthrough a previously exposed and developed hologram 42 which directs theultraviolet beam from source 41 into a pattern in a sensitized sample43, according to well-known holographic techniques. The pattern insample 43 as produced by hologram 42 in response to light from source 41results from focusing of the light as well as the exclusion of it fromcertain areas of the sample 43. This pattern of focused light produces athree-dimensional light guide network 44 in sample 43. This networkincludes the guides 44A, 44B and 44C. The guides 44A-44C may havecharacteristics similar to those disclosed above in connection with theguides described in FIGS. 1-3.

The exposure step of FIG. 4 may be characterized as a holographicexposure step; that is, the sensitized sample is holographically exposedto form the guide network 6 44A, 44B and 44C in a way which ispredetermined by the original formation of hologram 42.

Typically, a photographic film is exposed by interfering lightwavefronts or beams called the subject beam and the reference beam andthen developed to make hologram 42. The formation of hologram 42 is doneby methods which are now well known in the art and need not be discussedin detail here. For example, focusing holograms such as hologram 42 havebeen used heretofore in order to make two-dimensional photographicprints from holograms containing three-dimensional information.Specifically, focusing holograms such as hologram 42 are formed byexposing a suitable photographic film to a plane wave reference beam andan angularlydisplaced subject beam formed to simulate the desiredpattern, for example, to make the subject beam simulate guides 44A-44C.The feasibility of three-dimensional focusing with holograms is shown bythe IBM Technical Disclosure Bulletin, vol. 11, 1168 (February 1969) inthe article by T. J. OHara et al.

Our invention, and advantageously the species of FIG. 4, can be appliedto making optical memories, provided that the sample 43 has beensensitized in the manner according to the invention, as described above,and then, after exposure, is allowed to age after the manner of theinvention, as described above.

The exposure technique of FIG. 4 should not be confused with making ahologram in sample 43. Such possibilities are mentioned below.

Still a third variation of a method according to our invention may bepracticed with the aid of the apparatus shown in FIG. 5. Here again, theillustrated apparatus is mainly useful during the exposure step, thesensitization steps and aging steps being the same as heretofore.

Thus, for the exposure step, the apparatus of FIG. 5 includes thecontainer 51 filled with a liquid 52 which is typically a clear oilindex-matched with a fiber 53 of poly (methyl methacrylate) which is tobe formed into an optical guide according to the method of the presentinvention. Fiber 53 of poly(methylmethacrylate), of about twomicrometers diameter, is sensitized and polymerized at about 50 degreescentigrade as heretofore and then wound onto the supply spool 54. Fromthe supply spool, the fiber 53 is threaded over the first guidanceroller 55 of transparent index-matched material, thence under the secondguidance roller 56 of transparent index-matched material and therefromover the take-up spool 57, upon which it is aged after the manner of theinvention. It will be noted that guidance rollers 56 and 55 are immersedin the liquid 52 so that the fiber 53 extending therebetween iscentrally located in the body of the liquid.

The left-hand wall of container 51 has an ultraviolet lens 58 disposedtherein which serves to focus ultraviolet light from a suitable lasersource 59 upon the fiber 53 midway between rollers 55 and 56 in order toexpose it to create the transverse variation of index of refractionsuitable for a guide.

As in the previous exposure steps, the intense ultraviolet light at thewaist of the focused beam has an intensity sufiicient to create a changein index such that the index is greatest at the center of the fiber andleast at the edge of the fiber, with the total difference in indexbetween the center and the edge being about 5x10- or more generally, interms of the electric field, being about 1 X 10* XE E being theultraviolet energy for irradiation with 3250 A. light from the cadmiumion laser or being about for irradiation with 3650 A. light from themercury arc.

This exposure step differs from the previous exposure steps in that thesensitized medium, as it is exposed, is translated axially along thepath of the ultraviolet beam.

This collinear or axial translation is effective for the purposes of theinvention because the ultraviolet light outside the region of its waisthas an intensity too low to have substantial effect upon the index ofthe fiber according to the above-described approximately linearrelations between the change in index and ultraviolet energy. The waistdiameter of the beam is that minimum diameter, for an intensity of eofthe central or axial intensity, which occurs at the point along fiber 53at the theoretical focus point of the lens 58.

As the fiber 53 approaches the waist of the beam from the left, itexperiences very little index change until it enters a region extendingfor a few microns either way around the waist of the beam. It is thenexposed in an axially symmetrical manner. Thereafter, it is translatedout of the waist of the beam and experiences again very little effect,so that a very smooth and axially symmetrical transverse variation ofindex corresponding very closely to the gradient of light intensity atthe beam waist is obtained.

The fiber 53 is then wound up upon the take-up spool and aged thereon,after which it may be used for optical guiding of light of wavelengthoutside its range of photo sensitivity.

It will be noted that inadvertent damage to the index gradient isprevented by the ultraviolet absorber 60, which is disposed near thewall of container 51 opposite lens 58 to prevent reflection ofultraviolet light back toward fiber 53.

This exposure step readily may be described in detail mathematically;and the other exposure steps may be described by a somewhat modifiedanalysis.

Assuming that the ultraviolet light is produced by a laser of thehelium-cadmium ion type in the fundamental Gaussian mode at 3250 A., itis possible to describe the effective integrated density of radiationwithin the poly (methyl methacrylate) resulting from the various methodsof applying the radiation. By making a further assumption, namely, thatthe refractive index change at any point is directly proportional to theintegrated radiation intensity there, one can then arrive at an estimateof the equilibrium radius of the light beam traveling in a light guideformed by the ultraviolet radiation by each of the respective differentexposure steps.

An axially symmetrical Gaussian beam can be described by its powerdensity at a point z,r (where z is the distance from the waist of thebeam and r is the radial distance from the axis of the beam in a crosssection of the beam) by the following:

J1 r )=I p(z,0) being the power density on the axis at z, and w theso-called beam radius at z, i.e., the distance at which the amplitude ofthe radiation is eof the amplitude on the axis. The factor 2 in theabove equation accounts for the fact that we are dealing withintensities and not amplitudes.

w is given by the following:

where W is the beam radius at the waist, and Z is given y where A is thewavelength in the medium.

With the assumption of no loss in the medium, the principle ofconservation of energy leads to where p is the power density on the axisat the waist and is the highest power density in the beam.

It is easy to show that P, the total power in the beam, is given by 07 oIntroducing another dimensionless variable as follows:

A Gaussian beam with this intensity distribution in the medium, in whichthe refractive index is proportional to the incident radiation, willgive rise to a distribution of refractive index of identicalproportions, provided the index change is very small. It will be notedthat experimentally it has been observed that in the effective range ofexposure intensities, the refractive index change in the methods of thepresent invention is approximately proportional to the integratedincident radiation .(or ultraviolet energy). Therefore, Equation 6appears to be applicable to the distribution of change in refractiveindex.

In a plurality of our methods, we envisage relative motion between thebeam and the medium; and at least two of these motions have beendescribed in the embodiments of FIGS. 1 and 5. A third motion that couldbe used would be the rotation of the medium about an axis perpendicularto and intersecting the beam axis. This could be achieved in theembodiment of FIG. 5 if the spacing between rollers and 56 wereeliminated so that, in essence, there was a single guidance roller. Ofcourse, it would also be possible to use combinations of the motionsemployed in FIG. 1 in FIG. 5 and in the just-described modification ofFIG. 5.

A further mathematical analysis of the transverse motion employed inFIG. 1 can be employed to provide a description of the relative powerdensity ratio which is effective in providing a corresponding linearlyrelated change in index An. The following is the power density ratio Dwhere X =x/ W and as before.

The contours of equal power density ratios between zero and nine-tenthsresemble ellipses when both X and Z are small. One can then expandEquation 8 in powers of X and Z.

D, -1%Z-2X*+%Z+X*+2X+ (9) where it is assumed that the refractive indexchange is proportional to the electric field intensity.

Equation 9 shows that for small enough values of X and Z the irradiatedmedium of FIG. 1 or FIG. 4 is like a lens-like optical guide, althoughit is not a rotationally symmetrical one as has been commonly employedin the optical guiding art. This lack of the usual rotational symmetrymeans that an optical mode propagating in such a guide will haveelliptical symmetry rather than circular symmetry. The quasi-ellipticalcontours of equal power density can be described by their axes asfollows:

At this point it is convenient to recall that the half angle ofconvergence of a Gaussian beam is given by 0, W100 so that one can writeIt is not unexpected that one has to use a beam with a very largeconvergence half angle (which means a very low f/number lens) if onewishes to obtain a guide cross section, according to the method of FIG.1 and FIG. 4, with proportions not too different from 2:1.

The difference in the refractive index distribution in a guide withelliptical symmetry as contrasted to one with the more circular symmetryresides mainly in the consideration that we shall now have to considerbeam axes separately in two orthogonal coordinates, at least for theexposure steps employed in FIGS. 1 and 4.

Let us describe the refractive index distribution due to irradiation bywhere Art is the maximum change at the waist of the irradiating beam. Anapproximate equation for the equilibrium beam radius w in the zdirection is given by the following:

where x is the wavelength of the guided light.

On the other hand, an approximate equation for the equilibrium beamradius in the x-direction is as follows:

A better answer with respect to these parameters could be obtained froma solution of the wave equation from the actual refractive indexdistribution, perhaps by the means of the Fox and Li computationalmethod, as set forth in their well-known article on focusing lens-likemedia, Resonant Modes in a Maser Interferometer, Bell System TechnicalJournal, 40, 443 (1961).

For the axial translation of a sample 53 in FIG. 5 with respect to theultraviolet laser beam which performs the exposure step, a similar setof calculations may be carried out which will provide a solution of therelative or normalized power density as given by the following equation:

so that 11= o( where as before, and the other quantities are as definedabove.

When R is 1,

which shows again that for small values of R a medium in which therefractive index is proportional to the applied ultraviolet intensitywill act like a lens-like medium. In contrast to the analysis made abovefor FIGS. 1 and 4, the radial intensity distribution obtained in thiscase is circularly symmetrical and approximates much more closely thesort of index distribution which produces guiding in a gaseous opticalguide, that is, the radial intensity distribution is very close to thedesired quadratic distribution.

It should be understood that the index distributions described above arequite useful for optical guiding and produce relatively little modeconversion. The degree of mode conversion presently observedexperimentally is primarily due to the effects of surfaces at theentrance and exit of the guide and not due to the converting ordistorting influences of the transverse refractive index distributionwithin the guide. Thus it is considered that optical guides madeaccording to all of the above-described methods are practical and usefulfor the purpose of guiding visible light beams of suitable wavelength,as described above.

It should also be understood that mode conversions due to effects at theentrance and exit of the guide can be reduced by improving the qualityof the entrance and exit surfaces, which is a matter of ordinary skillin the art, inasmuch as those surfaces can be prepared carefully andthen highly polished and anti-reflection-coated. Mode conversions canalso be reduced by using other methods for coupling into the lightguides.

Our analysis shows that all the above-described specific methods fallinto the. generic method set forth in flow diagram form in FIG. 6. Thus,in the first step, the sample is sensitized to the ultraviolet radiationto which it is to be exposed. Typically, the sensitization stepaccording to our invention involves the inclusion of peroxides in anacrylate to enable photo-induced cross-linking in the poly(acrylate). Itis typically followed by the polymerization step, although the order ofthese steps may not be critical.

In the exposure step, the sensitized sample is then irradiated withfocused ultraviolet light having its greatest intensity where the guideis to be formed. The ultraviolet light is chosen to promote the furtherstructural development of the complex molecules such as the crosslinkingof some molecules among the molecules in the sensitized sample.

In the final step the optical guide or patterns of optical guides in thesample is then completed, typically by aging. The period of time forwhich aging ma be appropriate will depend upon the particularsensitization and exposure of the sample.

While we do not wish our invention to be limited by the followingtheoretical explanation, this tentative explanation tends to correspondto our experimental observations.

During exposure, it is believed that the ultraviolet light is absorbedby the peroxides to form active radicals that promote cross-linking ofthe polymer chains. It can be appreciated that the molecular structuralprocess of crosslinking would increase the density in the exposedregions.

Moreover, it appears that the cross-linking initially creates stressesthat tend to pull the polymer chains together. The material tends toresist these stresses, so that strains are set up in the sample duringexposure. These strains can be relieved and the stresses reduced by theflow of material into the irradiated region from the surrounding region;but much of the inflow may not occur immediately. Thus, the initialincrease in density is attributable to the cross-links and associatedimmediate displacement of material.

In any event, during exposure the density of the ma terial rises in theexposed region and indicates a more complex structure.

During the aging step, the last-described cross-linking or otherstructural change during exposure produces strains and resultingstresses in the sample where it was exposed, as mentioned above.Relaxation of the strains and consequent decrease of the stresses couldthen take place by the flowing of material into the irradiated areasover a period of time. The result is a further increase in the densityand index of refraction in those areas and a steeper gradient of thosequantities.

From the foregoing explanation, the peroxides are important duringexposure and the initiator plays no role. It would appear desirable toconvert all of the remaining stable initiator by-product remainingoutside the guides to a form not capable of response to a later exposureto ultraviolet exposing radiation. The achievement of this objective canbe obtained partially b using as small an amount of initiator in thestarting sample as will produce the above-described results.

Suitable starting materials for the generic method of FIG. 6 shouldinclude a large number of plastics which are useful for opticaltransmission and susceptible to photochemical change in index ofrefraction. We suggest polymethyl methacrylate and other methacrylatesand acrylates, as some alternatives. In some of these substances,radiation at wavelength outside the ultraviolet band may also be able toinduce the index change. In those cases the radiation to be guided willtypically be of longer wavelength than the exposing radiation, althoughit could also be a shorter, non-damaging wavelength. In addition, forsome of these other materials, particle radiation such as electrons orneutrons may also be effective to perform the exposure step and willadvantageously be employed according to our invention, in that theexposure step will be preceded by the sensitization step and followed bythe aging step.

It should also be observed that the method according to our inventionmay also be useful in forming an optical memory. The method of formingan optical memory according to our invention will differ from themethods of making optical memories by optical damage in lithium niobate,as discussed above, in that the sample is sensitized and then thecompleted index changes are aged aeccording to the method of ourinvention. The exposure step would not differ substantially from that ofprevious optical memory proposals employing index changes in transparentmedia. Of course, such index changes can be accomplished in threedimensions, thereby providing a very large total volume and a very highdensity of information storage.

In addition, our method can be used to produce threedimensionalholograms for general use. In this case, interfering subject andreference beams of coherent ultraviolet light are used to expose thesensitized sample.

A further modification of our invention resides in the fact that thewavelength range for exposure for poly(methyl methacrylate) sensitizedaccording to our invention extends throughout most of the range of thesoft ultraviolet which we have been able to investigate, namely, fromabout 4000 A. to about 2800 A. Other materials of course, will have asomewhat different range of exposure response. Furthermore, othersensitizers may be added to poly (methyl methacrylate) and to otherplastics, poly(acrylates) and polymerizable materials to make itpossible to effect the exposure step with visible rather thanultraviolet radiation.

Further applications of our invention are suggested in FIGS. 7 and 8.

It is often necessary to produce resonant reflectorsa means forreflecting light of particular wavelengthin optical waveguide or otherapplications. See S. E. Millers above-cited Bell System TechnicalJournal articles; also H. Kogelnik, Bell System Technical Journal, 48,2909 (1969). Such reflection may be produced by creating a series ofparallel planes of alternating high and low refractive index, withspacing d between equivalent planes, to form a Lippmanu-Bragg reflector.The means for ac- 12 complishing the required index variation inpoly(methyl methacrylate) is shown in FIGS. 7 and 8 where twoultraviolet beams, which may be derived from the same laser by beamsplitters, intersect at an angle 20. The interplanar spacing is governedby the Bragg formula where 0 -48 for poly(methyl methacrylate). Then,the input surfaces in FIG. 6 must be polished at an angle oblique to thereflecting planes.

Alternatively, the beam incident from below can be eliminated, and theinterfering beam will be produced by total reflection of the upper beamfrom the lower surface. In general, in FIG. 7, the surfaces of thesample may be at oblique angles to the reflecting planes. For example,diffraction gratings would be made by the method of our invention, withthis adaptation.

FIG. 8 differs from FIG. 7 in that the parallel planes of high and lowindex are not bounded by any surfaces of the sample. This figure showsthat the sample surfaces can be substantially removed from thereflecting parallel planes.

Such parallel planes of high and low index may also serve asone-dimensional guides for light entering (e.g., from the left) betweenthem at more than the critical angle 0,, with respect to their normal.Thus, the device of FIG. 8 can be either a reflector or a guide. In thelatter case, parallel polished sample surfaces 84 and 85 are providednormal to the parallel planes of elevated index. Light to be guided canthen be easily introduced.

We claim:

1. A composition of matter of the type including selected regions ofelevated index of refraction suitable for guiding an optical beam, saidcomposition of matter being produced by the process comprising the stepsof sensitizing a starting sample of a transparent polymerizable acrylateby introducing a peroxide therein to provide subsequent molecularstructural change tending to increase the index of refraction thereofupon exposure to ultraviolet radiation,

polymerizing said sample at a temperature below C. which does not impairthe sensitization of said sample provided in said sensitizing step,

exposing said sample to focused ultraviolet radiation to produce thereinregions of increased index of refraction in a selected pattern, and

completing the index change in said regions by aging said sample torelieve strains therein and to promote the migration of material intosaid regions.

2. A composition of matter according to claim 1 in which said peroxideis selected from the group consisting of dicumyl peroxide andtertiary-butyl perbenzoate.

3. A composition of matter according to claim 1 in which saidtransparent polymerizable acrylate is methyl methacrylate.

References Cited UNITED STATES PATENTS 2,553,325 5/1951 Loritsch 26089.5A 3,053,742 9/1962 Smith 204-159.l4 3,689,264 9/1972 Chandross et a196-351 HARRY WONG, J 11., Primary Examiner US. Cl. X.R.

